Question: Simplify the following expression: $\dfrac{110a^4}{44a}$ You can assume $a \neq 0$.
$ \dfrac{110a^4}{44a} = \dfrac{110}{44} \cdot \dfrac{a^4}{a} $ To simplify $\frac{110}{44}$ , find the greatest common factor (GCD) of $110$ and $44$ $110 = 2 \cdot 5 \cdot 11$ $44 = 2 \cdot 2 \cdot 11$ $ \mbox{GCD}(110, 44) = 2 \cdot 11 = 22 $ $ \dfrac{110}{44} \cdot \dfrac{a^4}{a} = \dfrac{22 \cdot 5}{22 \cdot 2} \cdot \dfrac{a^4}{a} $ $\phantom{ \dfrac{110}{44} \cdot \dfrac{4}{1}} = \dfrac{5}{2} \cdot \dfrac{a^4}{a} $ $ \dfrac{a^4}{a} = \dfrac{a \cdot a \cdot a \cdot a}{a} = a^3 $ $ \dfrac{5}{2} \cdot a^3 = \dfrac{5a^3}{2} $